The Rule of 2 and 4

"The majority of players are looking for reasons to fold.  I am looking for reasons to play."  ~ Daniel Negreanu

The Rule of 2 and 4 are quick shortcuts to help us work out the percentage needed to get a draw in Texas No-Limit Hold'em.  These shortcuts aren’t exact.  However, they are good enough for doing quick probabilities in our head at the tables.

The Rule of 2
The Rule of 2 states: Multiply your number of outs by 2 to get the approximate percentage of a draw you have on the turn or the river.   

For example, let's say you have a flush draw after the flop. 

• There are 2 cards of the same suit in your hand and 2 cards of the same suit on the board. 
  That makes 4 cards to a flush. 
• There are 13 cards to a suit, and 9 cards (outs) that can help you make a flush (13 - 4 = 9).
• Use the Rule 2 to approximate your percentage of hitting a flush on the next card.
  2 x 9 = 18% probability of getting your flush. 
  
  

The exact calculation is:

• There are 13 cards to a suit, and 9 cards (outs) that can help you make a flush (13 - 4 = 9).
• There are 52 cards in the deck minus 2 cards in your hand and 3 cards on the board.
• This leaves 47 cards remaining (52 - 5 = 47).
• (9/47) = 19% probability of getting your flush.

The Rule of 2 works because there are 52 cards in the deck
 and 52 goes into one hundred approximately twice.

The Rule of 4
The Rule of 4 is used when you are considering an all-in move after the flop and will see both the turn and river cards.  Multiply your number of outs by 4 to get the approximate percentage of a draw.
 
Like the Rule of 2 example,  you have a flush draw after the flop. 

• There are 2 cards of the same suit in your hand and 2 cards of the same suit on the board. 
  That makes 4 cards to a flush. 
  There are 13 cards to a suit, you have 9 cards (outs) remaining that can help you make your flush (13 - 4 = 9).
• Use the Rule 4 to approximate your percentage of hitting a flush on the next two cards.
  4 x 9 = 36% probability of making your flush. 
  
  

The exact calculation is as follows:

• There are 52 cards in the deck minus 2 cards in your hand and 3 cards on the board. 
  Consequently, there are 47 cards remaining (52 – 2 – 3 = 47).
• There are 9 cards that will help you make your flush. 
  Thus, there are 47 - 9 = 38 cards that will not make your flush on the turn.
• The probability of not making your flush on the turn is 38/47.   
• Subtract one from the numerator and denominator for the river card which is 37/46.
• Multiply both numbers together and subtract from 1 to determine your probability of making a flush.
• 1- 38/47 x 37/46 = 35% probability of making your flush.

Once again, that’s close and useful for quick estimate at the tables.

Note: The Core Math Chapter of Mastering Poker Math provides more detail on how this equation is derived.